The maximum value of basic inequality a,b＞0.ab≥1+a+b Find the minimum of a + B?

1+a+b≤ab≤[(a+b)/2]²
∴1+a+b≤(a+b)²/4
∴(a+b)²-4(a+b)-4≥0
The solution is: a + B ≥ 2 + 2 √ 2 or a + B ≤ 2-2 √ 2
∵a,b>0
∴a+b≥2+2√2
If and only if a = b = 1 + √ 2, the minimum value of a + B is 2 + 2 √ 2

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